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Signal-to-Noise Ratio Calculator

Calculate a signal-to-noise ratio in decibels from RMS amplitudes, powers, or a mean and standard deviation, and convert a dB value back to ratios.

Formula

SNR=AsignalAnoise\mathrm{SNR} = \dfrac{A_{\text{signal}}}{A_{\text{noise}}}
SNR (dB)=20log⁡10AsignalAnoise\mathrm{SNR}\,(\mathrm{dB}) = 20\log_{10}\dfrac{A_{\text{signal}}}{A_{\text{noise}}}
SNR (dB)=10log⁡10PsignalPnoise\mathrm{SNR}\,(\mathrm{dB}) = 10\log_{10}\dfrac{P_{\text{signal}}}{P_{\text{noise}}}
SNR (dB)=6.02 N+1.76(ideal converter)\mathrm{SNR}\,(\mathrm{dB}) = 6.02\,N + 1.76\quad(\text{ideal converter})
AA
RMS amplitude
PP
power
NN
bits of an ideal converter

How it works

The signal-to-noise ratio compares the size of the wanted signal with that of the unwanted noise. It is a ratio of amplitudes, or of powers, which is the square of the amplitude ratio, and is commonly expressed in decibels, where every 20 dB is a factor of ten in amplitude.

As statistics, the mean divided by the standard deviation is used as a signal-to-noise ratio for imaging and some detectors. The tool also shows the number of bits of an ideal converter whose quantisation noise alone would give the same SNR, which is how far a signal chain resolves a signal.

Worked example

A signal of 1.2 V RMS with noise of 15 mV RMS.

  1. Amplitude ratio = 1.2 / 0.015 = 80.
  2. SNR = 20 log₁₀(80) = 38.06 dB.
  3. Equivalent bits = (38.06 − 1.76) / 6.02 = 6.0.

The SNR is 38.06 dB, about 6 bits of ideal resolution.

These are the values the calculator opens with, so you can check its output against this example.

Assumptions

  • RMS values, measured over the same bandwidth for signal and noise.
  • Noise is uncorrelated with the signal.

Common mistakes

  • Using 10 log₁₀ for an amplitude ratio or 20 log₁₀ for a power ratio.
  • Using peak amplitudes in place of RMS.
  • Comparing SNRs measured over different bandwidths.

Related tools

Decibel CalculatorRatios to dB, dB to ratios, and dBm to powerOpen calculatorADC Resolution CalculatorLSB size, ideal SNR, bits needed, and effective bitsOpen calculatorSampling Frequency CalculatorSampling rate, record size and frequency resolutionOpen calculator

Related equipment

Service documentation, failure modes and parts for the instruments this calculation is used with.